测验

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\begin{center}
  {\LARGE\bfseries Quiz 3: Integration Techniques}\\[4pt]
  {\large MATH 1220, Calculus II}\\[2pt]
  Time allowed: 20 minutes \quad | \quad 10 points total
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\vspace{0.5em}
Name: \rule{2.8in}{0.4pt} \hfill Student ID: \rule{1.5in}{0.4pt}

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  title=\textbf{Instructions}]
  \begin{itemize}[leftmargin=1.2em, itemsep=1pt, topsep=1pt]
    \item Closed book. No calculators, notes, or electronic devices.
    \item Circle exactly one answer for each question.
    \item Each question is worth 2 points. There is no penalty for guessing.
    \item Stop writing when time is called.
  \end{itemize}
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\vspace{1.2em}
\begin{enumerate}[label=\textbf{\arabic*.}, leftmargin=2em, itemsep=1.2em]

\item What is $\displaystyle\int \frac{1}{x}\,dx$ for $x \neq 0$?
  \begin{enumerate}[label=(\alph*), itemsep=1pt]
    \item $\ln|x| + C$
    \item $\dfrac{1}{x^2} + C$
    \item $-\dfrac{1}{x^2} + C$
    \item $x \ln x + C$
  \end{enumerate}

\item The derivative of $e^{3x}$ is
  \begin{enumerate}[label=(\alph*), itemsep=1pt]
    \item $e^{3x}$
    \item $3e^{3x}$
    \item $\frac{1}{3}e^{3x}$
    \item $3xe^{3x-1}$
  \end{enumerate}

\item Using integration by parts, $\displaystyle\int x e^{x}\,dx$ equals
  \begin{enumerate}[label=(\alph*), itemsep=1pt]
    \item $\frac{1}{2}x^2 e^{x} + C$
    \item $x e^{x} + e^{x} + C$
    \item $(x - 1)e^{x} + C$
    \item $(x + 1)e^{x} + C$
  \end{enumerate}

\item Which substitution best evaluates $\displaystyle\int \frac{2x}{1 + x^2}\,dx$?
  \begin{enumerate}[label=(\alph*), itemsep=1pt]
    \item $u = 2x$
    \item $u = 1 + x^2$
    \item $u = \tan x$
    \item $x = \sin u$
  \end{enumerate}

\item The value of $\displaystyle\int_0^{1} 3x^2\,dx$ is
  \begin{enumerate}[label=(\alph*), itemsep=1pt]
    \item $0$
    \item $\tfrac{1}{3}$
    \item $1$
    \item $3$
  \end{enumerate}

\end{enumerate}

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